New Tribological Ways Part 12 pdf

Identification of Discharge Coefficients of Orifice-Type Restrictors for Aerostatic Bearings and Application Examples 369 Two discharge coefficients can thus be defined, one for each of the two localized pressure drops. As for annular orifice systems, discharge coefficient C d,c for the first pressure drop p S – p T is calculated considering the supply orifice's circular section of diameter d as the air passage section. Discharge coefficient C d,a for the second pressure drop p T – p i is calculated by taking the annular section of height h and diameter d 0 as the passage section. When the pocket is sufficiently deep ( δ > 20 μm), the pressure drop at the air gap inlet is significant by comparison with that across the inlet hole, and in this case both the discharge coefficients must be defined. In all cases with δ ≤ 20 μm, p T ≅ p i and it is possible to define only coefficient C d,c . The theoretical air flow rate through each lumped resistance is given by equation (3): 21 2 1 2 if 0.528 1 22 if 0.528 11 k kk dd d tu uu u k d tu u PP P k GSP kP P RTP P k GSP kkRTP + − ⎡⎤ ⎛⎞⎛⎞ ⎢⎥ =⋅ − ⋅ ≥ ⎜⎟⎜⎟ ⎢⎥ −⋅ ⎝⎠⎝⎠ ⎢⎥ ⎣⎦ ⎛⎞⎛⎞ =⋅ ⋅ ⋅ < ⎜⎟⎜⎟ ++⋅ ⎝⎠⎝⎠ (3) where P u and P d are the resistances' upstream and downstream absolute pressures, T is the absolute temperature upstream of the nozzle, S is the passage section area, R = 287.1 J/(kg K) is the air constant, and k = 1.4 is the specific heat ratio of air at constant pressure and volume. As G t and G are known, the values of C d,c and C d,a were calculated using equation (1). In order to allow for the effect of geometric parameters and flow conditions on system operation, C d,c and C d,a can be defined as a function of the Reynolds number Re. Considering the characteristic dimension to be diameter d for the circular passage section, and height h for the annular passage section, the Reynolds numbers for the two sections are respectively: 4 Re c ρ u d G μπ d μ == ; 0 Re a ρ u h G μπ d μ == (4) where ρ , u and μ are respectively the density, velocity and dynamic viscosity of air. Figure 14 shows the curves for C d,c versus Re c obtained for the pads with annular orifice supply system (type "a") plotted for the geometries indicated in Table 1 at a given gap height. Each experimental curve is obtained from the five values established for supply pressure. Results indicate that supply orifice length l in the investigated range (0.3 mm – 1 mm) does not have a significant influence on C d,c . By contrast, the effect of varying orifice diameter and gap height is extremely important. In particular, C d,c increases along with gap height, and is reduced as diameter increases, with all other geometric parameters remaining equal. For small air gaps, C d,c generally increases along with Re c , and tends towards constant values for higher values of Re c . With the same orifices but larger air gaps, values of Re c numbers are higher: in this range, the curves for the C d,c coefficients thus obtained have already passed or are passing their ascending section. Figure 15 shows C d,c versus Re c obtained for the pads with simple orifices with feed pocket supply system (pads "b" and "c") for pressure drop p S – p T , plotted for the geometries indicated in Table 2 with δ = 10, 20, 1000 μm and at a given gap height. As the effects of New Tribological Ways 370 varying orifice length were found to be negligible, tests with feed pocket supply system were carried out only on pads with l = equal to 0.3 mm. The values for C d,c obtained with the simple orifices with feed pocket are greater than the corresponding coefficients obtained with annular orifice system, but the trend with Re c is similar. In particular, the same results shown in Figure 14 are obtained if δ tends to zero. If δ = 10, 20 μm C d,c is heavily dependent on h, d, δ: it increases along with gap height h and δ, and is reduced as diameter d increases, with all other geometric parameters remaining equal. If δ = 1 mm, values for C d,c do not vary appreciably with system geometry, but depend significantly only on Re c . For Re c → ∞, the curves tend toward limits that assume average values close to C d,c max = 0.85. Fig. 14. Experimental values for C d,c versus Re c obtained for type "a" pads Fig. 15. Experimental values for C d,c versus Re c obtained for type "b" and "c" pads, and with l = 0.3 mm Figure 16 shows C d,a versus Re a obtained for the pads with simple orifice and feed pocket supply system and with a non-negligible pressure drop p T – p i (type "b" pads). Here again, values for C d,a depend significantly only on Re a and tend towards the same limit value slightly above 1. This value is associated with pressure recovery upstream of the inlet resistance. In order to find formulations capable of approximating the experimental curves of C d,c and C d,a with sufficient accuracy, the maximum values of these coefficients were analyzed as a function of supply system geometrical parameters. Figures 17 and 18 show the experimental maximum values of C d,c from Figure 14 and Figure 15 respectively, as a function of ratio h/d and (h+ δ )/d. Figure 18 also shows the results of Figure 17 ( δ = 0) only for l = 0.3 mm. The proposed exponential approximation function is also shown on the graphs: ( ) ( ) 82 1 085 1 (h δ)/d) f [(h δ)/d] . -e + += (5) where δ = 0 for annular orifices. To approximate the experimental values of the discharge coefficients in the ascending sections of the curves shown in Figures 14 and 15, a function 2 f of h, δ, Re c is introduced: Identification of Discharge Coefficients of Orifice-Type Restrictors for Aerostatic Bearings and Application Examples 371 0 001 Re 4 2 1 c h δ . h δ f [(h δ)/d] e + −⋅ + ⎛⎞ ⎜⎟ +=− ⎜⎟ ⎝⎠ (6) The complete function proposed to identify C d,c thus assumes the following form: () ( ) 0 001 Re 82 4 12 085 1 1 c h δ . (h δ)/d) h δ d,c Cf f. -e e + −⋅ + + ⎛⎞ ⎜⎟ =⋅= ⋅− ⎜⎟ ⎝⎠ (7) The graphs in Figures 14 and 15 show several curves where all the values of coefficients C d,c are in a range equal to about 5% of the maximum calculated value. For these cases, it is assumed that the C d,c curves have already reached their limit, which is considered to be equal to the average calculated value. In the other curves, the values of C d,c do not reach their limits, to extrapolate these limits the values obtained with the highest Re c have been divided by the function f 2 and the results are shown in Figure 18. Experimental data for C d,c max can be grouped into three zones: zone I ((h+ δ )/d <0.1) for orifices with no pockets, zone II ((h+ δ )/d = 0.1 to 0.2) for shallow pockets, and zone III ((h+ δ )/d >0.2) for deep pockets. While C d,c max depends on h and δ in zones I and II, it reaches a maximum value which remains constant as (h+ δ )/d increases in zone III. In particular, when d is predetermined and δ is sufficiently large, C d,c max is independent of h. In this range, the supply system provides the best static bearing performance, as reducing air gap height does not change C d,c max and thus does not reduce the hole's conductance. However, excessive values for δ or for pocket volume can cause the bearing to be affected by dynamic instability problems (air hammering), which must be borne in mind at the design stage. The proposed exponential approximation function for C d,a in simple orifices with feed pocket is an exponential formula which depends only on Re a : ( ) 0 005 Re 105 1 a . d,a C. e − =⋅− (8) Fig. 16. Experimental values for C d,a versus Re a , for type "b" pads, with δ = 1 mm and d 0 = 2 mm Fig. 17. Maximum experimental values of C d,c and function f 1 (solid line) for pads with annular orifice, versus ratio h/d New Tribological Ways 372 The graphs in Figures 19-22 show a comparison of the results obtained with the these approximation functions. Specifically, Figures 19-20 give the values of C d,c for the annular orifices, while Figures 21 and 22 indicate the values of C d,c and C d,a respectively for the simple orifices with pocket. As can be seen from the comparison, the data obtained with approximation functions (7) and (8) show a fairly good fit with experimental results. Fig. 18. Maximum experimental values of C d,c and function f 1 (solid line) for the pad with simple orifices and feed pocket, versus ratio (h+ δ )/d Fig. 19. Experimental values (dotted lines) and approximation curves (solid lines) for C d,c versus Re c , for type "a" pads with l = 0.3 mm Fig. 20. Experimental values (dotted lines) and approximation curves (solid lines) for C d,c versus Re c , for type "a" pads with l = 0.6 mm and l = 0.9 mm Fig. 21. Experimental values (dotted lines) and approximation curves (solid lines) for C d,c versus Re c , for type "b" and "c" pads, and with l = 0.3 mm 6. Mathematical model of pads The mathematical model uses the finite difference technique to calculate the pressure distribution in the air gap. Static operation is examined. As air gap height is constant, the Identification of Discharge Coefficients of Orifice-Type Restrictors for Aerostatic Bearings and Application Examples 373 study can be simplified by considering a angular pad sector of appropriate amplitude. For type “c” pads, this amplitude is that of one of the supply holes. Both the equations for flow rate G (3) across the inlet holes and the Reynolds equations for compressible fluids in the air gap (9) were used. 22 33 0 2 11 24 0 PP G rh h R T rr r rdrd r μ ϑϑ ϑ ⎛⎞⎛⎞ ∂∂ ∂∂ + += ⎜⎟⎜⎟ ⎜⎟⎜⎟ ∂∂ ∂∂ ⎝⎠⎝⎠ (9) The Reynolds equations are discretized with the finite difference technique considering a polar grid of “n” nodes in the radial direction and “m” nodes in the angular direction for the pad sector in question. The number of nodes, which was selected on a case by case basis, is appropriate as regards the accuracy of the results. Each node is located at the center of a control volume to which the mass flow rate continuity equation is applied. Because of the axial symmetry of type “a” and “b” pads, flow rates in the circumferential direction are zero. In these cases, the control volume for the central hole is defined by the hole diameter for type “a” pads or by the pocket diameter for type “b” pads. The pressure is considered to be uniform inside these diameters. For type “c” pads, the center of each supply hole corresponds to a node of the grid. As an example for this type, Figure 23 shows a schematic view of an air gap control volume centered on generic node i,j located at one of the supply holes. Also for this latter type, several meshing nodes are defined in the pockets to better describe pressure trends in these areas. In types “b” and “c”, the control volumes below the pockets have a height equal to the sum of that of the air gap and pocket depth. For type “b”, which features very deep pockets, the model uses both formulations for discharge coefficients C d,c and C d,a , whereas for type “c” only C d,c is considered. qr i -1/2, j Gij q i , j+1/2 i, j+1 i-1, j q i , j-1/2 i, j i, j-1 qri +1/2, j i+1, j Fig. 22. Experimental values (dotted lines) and approximation curve (solid line) for C d,a versus Re a , for type "b" pads, δ = 1 mm, d 0 = 2 mm Fig. 23. Control volume below generic node i,j located on a supply hole of type “c” pad. The model solves the flow rate equations at the inlet and outlet of each control volume iteratively until reaching convergence on numerical values for pressure, the Reynolds number, flow rate and discharge coefficients. New Tribological Ways 374 7. Examples of application for discharge coefficient formulations: comparison of numerical and experimental results A comparison of the numerical results obtained with the radial and circumferential pressure distributions indicated in the graphs in Figures 9 – 12 will now be discussed. The selected number of nodes is shown in each case. For all simulations, the actual hole diameters for which pressure distribution was measured were considered. The data obtained with the formulation are in general similar or slightly above the experimental data, indicating that the approximation is sufficiently good. In all cases, the approximation is valid in the points located fairly far from the supply hole, or in other words in the zone where viscous behavior is fully developed, inasmuch as the model does not take pressure and velocity gradients under the supply holes into account. This is clearer for type “a” pads (Figure 24) than for type “b” and “c” pads, where the model considers uniform pressure in the pocket. For cases with deep pockets (type “b” pads), the numerical curves in Figure 25 show the pressure rises immediately downstream of the hole and at the inlet to the air gap due to the use of the respective discharge coefficients. For type “c” pads with pocket depth δ ≤ 20 μm (Figure 26), on the other hand, the pressure drop at the air gap inlet explained in the previous paragraph was not taken into account. In general, the approximation problems were caused by air gap height measurement errors resulting both from the accuracy of the probes and the difficulties involved in zeroing them. Thus, it was demonstrated experimentally that pressure in the air gap and flow rate are extremely sensitive to inaccuracies in measuring h. Significant variations in h entail pressure variations that increase along with average air gap height. Figure 27 shows another comparison of experimental and numerical pressure distributions for type “c” pads, this time with different air gap heights and pocket depths. 0 2 4 6 8 10 12 14 16 18 2020 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 10 5 Radial distance r [mm] Pressure [Pa] num h=9 μ m num h=14 μ m exp h=9 μ m exp h=14 μ m 0 2 4 6 8 10 12 14 16 18 20 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 10 5 Radial distance r [mm] Pressure [Pa] num h= 9 μ m num h = 14 μ m exp h = 9 μ m exp h = 14 μ m Fig. 24. Numerical and experimental radial pressure distribution across number "1" pad, type "a" , supply pressure p S = 0.5 MPa, orifice diameter d = 0.2 mm, air gap height h = 9 and 14 μm, n×m= 20×20. Fig. 25. Numerical and experimental radial pressure distribution across entire pad number "8", type "b", supply pressure p S = 0.5 MPa, orifice diameter d = 0.2 mm, pocket diameter d 0 = 2 mm, pocket depth δ = 1 mm, air gap height h = 9 and 14μm, n×m= 20×20. Identification of Discharge Coefficients of Orifice-Type Restrictors for Aerostatic Bearings and Application Examples 375 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 0 0.5 1 1.5 2 2.5 3 3.5 4 x 10 5 Radial distance r [mm] Pressure [Pa] num h = 11 μ m exp h = 11 μ m 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 10 5 Circumferential distance c [mm] Pressure [Pa] num h=11 μ m, δ =20 μ m exp h=11 μ m, δ =20 μ m num h=17 μ m, δ =20 μ m exp h=17 μ m, δ =20 μ m num h=11 μ m, δ =10 μ m exp h=11 μ m, δ =10 μ m num h=16 μ m, δ =10 μ m exp h=16 μ m, δ =10 μ m Fig. 26. Radial pressure distribution across pad number "11", type "c", supply pressure p S = 0.4 MPa, orifice diameter d = 0.2 mm, pocket diameter d 0 = 4 mm, pocket depth δ = 20 μm, air gap height h = 11 μm , n×m= 20×20. Fig. 27. Numerical and experimental circumferential pressure distribution across pad number "11", type "c", supply pressure p S = 0.5 MPa, orifice diameter d = 0.2 mm, pocket diameter d 0 = 4 mm, pocket depth δ = 10 and 20 μm, n×m= 20×20. Fig. 28. Further pads tested to verify the discharge coefficient formulation The discharge coefficient formulation was also verified experimentally on a further three pads as shown in the diagram and photograph in Figure 28, including two type “c” pads and one grooved pad (type “d”). Table 3 shows the nominal geometric magnitudes for each pad. The first two (13, 14) have a different number of holes and pocket depth is zero. The third (15) features 10 µm deep pockets and a circular groove connecting the supply holes. The groove is 0.8 mm wide and its depth is equal to that of the pockets. The figure also shows an enlargement of the insert and groove for pad 15 and the groove profile as measured radially using a profilometer. In these three cases, the center of the pads was selected as the origin point for radial coordinate r and the center of one of the supply holes was chosen as the origin point of angular coordinate ϑ. New Tribological Ways 376 In all cases, the actual average hole dimensions were within a tolerance range of around 10% of nominal values. A mathematic model similar to that prepared for type “c” pads was also developed for type “d”, considering the presence of the groove. Comparisons of the experimental and numerical pressure distributions for the three cases are shown in Figures 29 - 31. Pad N. Pad type n. holes Insert Groove Hole Pocket l [mm] d [mm] d 0 [mm] δ [μm] w g [mm] h g [μm] 13 c 6 0.4 0.2 4 0 - - 14 c 3 0.4 0.2 4 0 - - 15 d 3 0.4 0.3 4 10 0.8 10 Table 2. Nominal dimensions of pads 13, 14, 15. 5 7.5 10 12.5 15 17.5 20 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Radial distance r [mm] Pressure [Pa] Pad 13, θ = 0° num. exp x 10 5 5 7.5 10 12.5 15 17.5 20 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Radial distance r [mm] Pressure [Pa] Pad 13, θ =30° num. exp. x 10 5 Fig. 29. Numerical and experimental circumferential pressure distribution across pad "13”, supply pressure p S = 0.5 MPa, orifice diameter d = 0.2 mm, pocket diameter d 0 = 4 mm, pocket depth δ = 0 μm, air gap height h = 15 μm, θ = 0° and 30°, n×m= 21×72. 5 7.5 10 12.5 15 17.5 20 0 1 2 3 4 5 x 10 5 Radial distance r [mm] Pressure [Pa] Pad 14, θ =0° exp h=13 μ m num h=13 μ m exp h=18 μ m num h=18 μ m 5 7.5 10 12.5 15 17.5 20 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 x 10 5 Radial distance r [mm] Pressure [Pa] Pad 14, θ =60° exp h=13 μ m num h=13 μ m exp h=18 μ m num h=18 μ m Fig. 30. Comparison of experimental and numerical radial pressure distributions, pad "14", p S = 0.5 MPa, orifice diameter d = 0.2 mm, pocket diameter d 0 = 4 mm, pocket depth δ = 0 μm, air gap height h = 13 and 18μm, θ = 0° and 60°, n×m= 21×72. Identification of Discharge Coefficients of Orifice-Type Restrictors for Aerostatic Bearings and Application Examples 377 5 7.5 10 12.5 15 17.5 20 0 1 2 3 4 5 x 10 5 Radial distance r [mm] Pressure [Pa] Pad 15, θ =0° exp h=13 μ m num h=13 μ m exp h=18 μ m num h=18 μ m 5 7.5 10 12.5 15 17.5 20 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 x 10 5 Radial distance r [mm] Pressure [Pa] Pad 15, θ =60° exp h=13 μ m num h=13 μ m exp h=18 μ m num h=18 μ m Fig. 31. Comparison of experimental and numerical radial pressure distributions, pad "15", p S = 0.5 MPa, orifice diameter d = 0.3 mm, pocket diameter d 0 = 4 mm, pocket depth δ = 10μm, air gap height h = 13 and 18 μm, θ = 0° and 60°, n×m= 21×72. Here as in the previous cases, the numerical curves correspond with the experimental data or overestimate them slightly. For the pad with groove and pockets in particular, the width of the groove is slightly greater than the diameter of the supply holes and the pockets are sufficiently large to distance the groove from the holes. In this way, the influence of the groove on the air flow adjacent to the supply holes is negligible, the system’s behavior is similar to that of the type “c” pad, and the validity of the formulation is also confirmed for this case. It should be borne in mind, however, that reducing the size of the pockets and groove can have a significant influence on flow behavior around the supply holes. In cases where the formulation is not verified, it will be necessary to proceed with a new identification of the supply system. 8. Conclusions This chapter presented an experimental method for identifying the discharge coefficients of air bearing supply systems with annular orifices and simple orifices with feed pocket. For annular orifice systems, it was found that the flow characteristics can be described using the experimental discharge coefficient relative to the circular orifice section, C d,c . For simple orifices with feed pocket, the flow characteristics can be described using two experimental discharge coefficients: C d,c for the circular section of the orifice and C d,a for the annular section of the air gap in correspondence of the pocket diameter. In particular, for deep pockets with (h+ δ )/d ≥ 0.2, both coefficients apply, while for shallow pockets with (h+ δ )/d < 0.2, only coefficient C d,c applies. Analytical formulas identifying each of the coefficients were developed as a function of supply system geometrical parameters and the Reynolds numbers. To validate the identification, a finite difference numerical model using these formulations was prepared for each type of pad. Experimental and numerical pressure distributions were in good agreement for all cases examined. The formulation can still be applied to pads with a circular groove if sufficiently large pockets are provided at the supply holes. Future work could address supply systems with grooves and pockets with different geometries and dimensions. As pad operating characteristics are highly sensitive to air gap height, the identification method used calls for an appropriate procedure for measuring the air gap in order to ensure [...]... Marklund, O (1994) Measuring lubricant film thickness with image analysis, Proc Instn Mech Engrs., Part( J), J of Eng Tribology, 208, pp 199-205 Yang, P., Qu, S., Kaneta, M & Nishikawa, H (2001) Formation of steady Dimples in point TEHL contacts, ASME, J of Tribology, 123 , pp.42-49 402 New Tribological Ways Marklund, O (1998) A pseudo-phase stepping approach to interferometric measurements, TULEA:09... and successful method in measuring oil film Several studies of an EHL film were carried 382 New Tribological Ways out by experiments (Cameron & Gohar, 1966; Foord et al., 1968; Johnston et al., 1991; Gustafsson et al., 1994; Yang et al., 2001) Since the image processing technique requires a calibration, which always introduces errors, the multi-channel interferometry method was proposed by (Marklund... exact )max (%) ΔTm exact D.I -12. 477 26.587 44.270 I.A 3.480 6.601 8.908 ( ΔTa present − ΔTa exact )max (%) ΔTa exact D.I -3.240 7.205 13.283 I.A 1.797 3.833 5.571 ( ΔTb present − ΔTb exact )max (%) ΔTb exact D.I -3.527 7.690 13.983 I.A 1.858 3.969 5.786 Table 3 Effect of film thickness measurement error on pressure and temperature ( −1 < X < 1 ) 392 New Tribological Ways 4.2 Inverse approach solution... the apparent viscosity of lubricants can also be obtained Fig 12 shows the dimensionless apparent viscosity versus the X-coordinate for various simulated measurement errors in the film thickness The results show that the present algorithm still gives a reasonable solution for the apparent viscosity By contrast, use of the 396 New Tribological Ways Fig 10 Pressure distributions and film shapes for different... of Line Contacts Fig 11 Temperature rise distributions for different standard deviations of the measured errors with 31 measured points in the film thickness using inverse approach 397 398 New Tribological Ways Fig 12 Comparison of dimensionless apparent viscosity between two algorithms with implemented errors Inverse Approach for Calculating Temperature in Thermal Elasto-Hydrodynamic Lubrication of... 380 New Tribological Ways Fourka, M.; Tian, Y.; Bonis, M (1996) Prediction of the stability of air thrust bearing by numerical, analytical and experimental methods Wear, 198, (1-2), pp 1-6 Goodwin, M.J (1989) Dynamics of rotor-bearing systems, Unwin Hyman, London Grassam, N S.; Powell, J W (1964) Gas Lubricated Bearings, Butterworths, London, pp 135-139 Gross, W.A (1962) Gas film lubrication, Wiley, New. .. Temperature calculation The temperature distribution within an oil film can be solved by the energy equation subject to appropriate boundary conditions Neglecting heat convection across the film and 386 New Tribological Ways circumferential conduction in the film, the energy equation for line contact problems may be written as: 2 ⎛ ∂u ⎞ ∂p ∂ ⎡ ∂T ⎤ ∂T −η ⎜ ⎟ − Tβ u ⎢κ ⎥ = ρ c pu ∂y ⎣ ∂y ⎦ ∂x ∂y ⎠ ∂x ⎝ (18) Adding... the estimated values of the pressure and the temperature rise become quite accurate in the pressure spike region It is clear that the direct inverse method requires a lot of measured points 388 New Tribological Ways Fig 2 Pressure distributions for different measured points in the film thickness using direct inverse method Fig 3 Temperature rise distributions for different measured points in the film... pressure fluctuations can be found everywhere If this pressure distribution is used to solve the temperature rise distribution, the error in the temperature rise should be also found everywhere 390 New Tribological Ways Fig 4 Pressure distributions for different standard deviations of the measured errors with 169 measured points in the film thickness using direct inverse method Inverse Approach for Calculating... International, 32, (12) , pp 731-738 Yoshimoto, S.; Kohno, K (2001) Static and dynamic characteristics of aerostatic circular porous thrust bearings Journal of Tribology, 123 , (7), pp 501-508 Yoshimoto, S., Tamamoto, M.; Toda, K (2007) Numerical calculations of pressure distribution in the bearing clearance of circular aerostatic bearings with a single air supply inlet, Transactions of the ASME, 129 (4), pp . indicated in Table 2 with δ = 10, 20, 1000 μm and at a given gap height. As the effects of New Tribological Ways 370 varying orifice length were found to be negligible, tests with feed pocket. C d,c and function f 1 (solid line) for pads with annular orifice, versus ratio h/d New Tribological Ways 372 The graphs in Figures 19-22 show a comparison of the results obtained with. numerical values for pressure, the Reynolds number, flow rate and discharge coefficients. New Tribological Ways 374 7. Examples of application for discharge coefficient formulations: comparison